I have tried the browser mining option when it was released as an experimental effort long time back ( just out of curiosity). But since it uses the CPU ( and not the GPU - even if you had one ), it will definitely be not worth the power / time . ( IMHO)
If you are using chrome, Shift + Esc will show you what component in your browser is using up your CPU - and if you are mining using the browser, it will show that its eating up most of your resources.
You do realize that you are almost certainly paying more for electricity than you are earning using a browser miner? There are much, much better ways to make money. Browser mining is just one step away from being faucet tier shit. Why not invest in some decent hardware so you can mine properly, or if you can't afford it, save up your money and pay for a cloud mining account.
Going back into your suggestion i would rather save up money than on investing on cloud mining site. If you go that path you are still wasting up your money.
You're missing the point of browser mining. There's a slider control that allows you to reduce the % usage so you can mine in the background and still use your PC. If you just measure the extra electricity the mining process uses then with average electricity prices it should be profitable. It only really works for a PC that is already turned on.